Second-order time-dependent mild-slope equation for wave transformation
type: Item
instance of: scholarly article
title: Second-order time-dependent mild-slope equation for wave transformation
zbMATH Open document ID: 1407.86006
DOI: 10.1155/2014/341385
author: Ching-Piao Tsai
author: Hongbin Chen
author: John R. C. Hsu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This study is to propose a wave model with both wave dispersivity and nonlinearity for the wave field without water depth restriction. A narrow-banded sea state centred around a certain dominant wave frequency is considered for applications in coastal engineering. A system of fully nonlinear governing equations is first derived by depth integration of the incompressible Navier-Stokes equation in conservative form. A set of second-order nonlinear time-dependent mild-slope equations is then developed by a perturbation scheme. The present nonlinear equations can be simplified to the linear time-dependent mild-slope equation, nonlinear long wave equation, and traditional Boussinesq wave equation, respectively. A finite volume method with the fourth-order Adams-Moulton predictor-corrector numerical scheme is adopted to directly compute the wave transformation. The validity of the present model is demonstrated by the simulation of the Stokes wave, cnoidal wave, and solitary wave on uniform depth, nonlinear wave shoaling on a sloping beach, and wave propagation over an elliptic shoal. The nearshore wave transformation across the surf zone is simulated for 1D wave on a uniform slope and on a composite bar profile and 2D wave field around a jetty. These computed wave height distributions show very good agreement with the experimental results available.
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 76M12
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 7016195
Wikidata QID: Q59064350
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/341385
OpenAlex ID: W2009089620
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description: scientific article; zbMATH DE number 7016195